The more I heard what my students noticed and wondered and more I thought about it, the more I like the analogy between learning archery and learning calculus or history or engineering or any other class at university.
Let’s Learn Archery!
(I’ve never shot an arrow, other than the usual bendy sticks and string thing that kids do during their summer holidays, so I could be totally *ahem* off-target here. If you know about archery, please, leave me a comment!)
Let’s suppose you want to learn archery. At first, the archery instructor will give you some direct instruction to get you to a level where you’re able to safely shoot an arrow in the general direction of the target. Now it’s your turn to practice and build your skills.
But imagine this: Imagine that the archery target is just the bull’s-eye. A little red circle, what, a couple of inches across, at the other end of the archery range. What kind of assessment and feedback would you get when you practice? You’d know when you did things 100% correct and hit the bull’s-eye. Otherwise, nothing. That would be frustrating and I suspect you’d give up. (Did you try Flappy Bird? And get angry and delete it? Yeah, like that.)
What’s so cool about a real archery target, then, is the instantaneous and formative feedback it gives you. When your arrow hits the target, you know immediately how you’re preforming (how close to bull’s-eye are you?) and, more importantly for learning, what you need to do to improve your aim. Hit up and to the left? Next time, aim more down and to the right.
You know what else is cool? It’s obvious and “well, d’uh, what else could it be?” that it’s you shooting the arrows, not the instructor. Sure, it would be extremely valuable to watch an expert, especially as you learn what to look for, but in the end, you have to do it yourself.
Let’s Learn Calculus!
After all that fun at the archery range, it’s time to head home. That calculus homework’s not going to do itself, you know. Imagine the instructor gives you a list of questions to do each week (“all the even numbered questions at the end of Chapter 7”). You work through them, and hand them in.
The teaching assistants don’t have time to mark your homework thoroughly. The most they can do is look at your answers to Questions 4, 6 and 12 and give you a check mark or an X. What kind of assessment and feedback would you get from this? That you’re 100% correct on some questions, wrong on a few others, and nothing at all on the rest.
I’m not trying to pick on math. I’ve heard students say they only feedback they get on an essay is a letter grade on the front page.
How is anyone supposed to learn from that?
The feedback helps students learn calculus and history and whatever they’re studying depends critically on the discipline. Each field, each course has its own set of skills and/or attitudes. The instructor’s job is to help the students become more expert-like. There are some underlying patterns to the practice and formative assessment that support learning, though. These are drawn from Chapter 5 of a great book, How Learning Works, by Susan Ambrose et al. (2010):
- practice needs to be goal-directed: everything the instructor asks students to do should support one or more of the course’s learning outcomes. If the assignment doesn’t, why are the students wasting their time on it?
- practice needs to be productive: the students need to get something out of everything they do. Do they really need to answer twenty questions at the back of Chapter 7? What about 5 representative questions from Chapter 7, plus 4 questions from Chapter 6 and 3 questions from Chapter 5 so they also get some practice at retrieving previous concepts (like they’ll have to do on, say, the final exam!)
- feedback needs to be timely: when do I need feedback on the aim of my arrow? Right now, before I shoot another one. Not in 2 weeks when the TAs have finally been able to finish marking all the papers and entered the grades.
- feedback needs to be at an appropriate level: A checkmark, a letter grade, or only circling the spelling mistakes are not sufficient. Neither is referring the student to the proof of Fermat’s Last Theorem. A good rubric, for example, lets each student know what they’re acheiving and also what success looks like at this level.
Frequent productive, goal-directed practice with timely, formative feedback at an appropriate level. That’s what an archery target gives you. We need to find the target in each course we teach.
What does the target it look like in your course?